Bozbura, beskese 2007 - prioritization of organizational capital measurement indicators using fuzzy ahp

1. Prioritization of organizational capital
measurement indicators using fuzzy AHP
F. Tunç Bozbura, Ahmet Beskese *
Department of Industrial Engineering, Bahcesehir University, 34100, Besiktas, Istanbul, Turkey
Received 29 September 2005; received in revised form 10 July 2006; accepted 18 July 2006
Available online 18 August 2006
Abstract
Organizational capital is a sub-dimension of the intellectual capital which is the sum of all assets
that make the creative ability of the organization possible. To control and manage such an important
force, the companies must measure it first. This study aims at defining a methodology to improve the
quality of prioritization of organizational capital measurement indicators under uncertain conditions.
To do so, a methodology based on the extent fuzzy analytic hierarchy process (AHP) is applied.
Within the model, three main attributes; deployment of the strategic values, investment to the tech-
nology and flexibility of the structure; their sub-attributes and 10 indicators are defined. To define the
priority of each indicator, preferences of experts are gathered using a pair-wise comparison based
questionnaire. The results of the study show that ‘‘deployment of the strategic values’’ is the most
important attribute of the organizational capital.
2006 Elsevier Inc. All rights reserved.
Keywords: Organizational capital; Measurement indicators; Fuzzy sets; AHP; Prioritization
1. Introduction
Knowledge is a vital resource in any organization. It can be used to improve quality and
customer satisfaction, and decrease cost in every meaning, if managed properly. Consid-
ering this management of knowledge, be it explicit or tacit, is a necessary prerequisite
for the success in today’s dynamic and changing environment [1].
0888-613X/$ - see front matter 2006 Elsevier Inc. All rights reserved.
doi:10.1016/j.ijar.2006.07.005
*
Corresponding author. Tel.: +90 212 381 0561; fax: +90 212 236 3188.
E-mail address: beskese@bahcesehir.edu.tr (A. Beskese).
International Journal of Approximate Reasoning
44 (2007) 124–147
www.elsevier.com/locate/ijar

2. AS Wong and Aspinwall state in their paper: ‘‘As knowledge emerges as the primary
strategic resource in the 21st century, many firms in the manufacturing and service sectors
alike are beginning to introduce and implement Knowledge Management (KM). Organi-
zations can certainly benefit from its application for enhanced decision support, efficiency
and innovation, thus helping them to realize their strategic mission. However, KM is an
emerging paradigm, and not many organizations have a clear idea of how to proceed with
it.’’ [2]
An OECD report on measuring KM in the business sector defines the KM concept as in
the following: ‘‘KM covers any intentional and systematic process or practice of acquiring,
capturing, sharing and using productive knowledge, wherever it resides, to enhance learn-
ing and performance in organizations. These investments in the creation of ‘‘organiza-
tional capability’’ aim at supporting – through various tools and methods – the
identification, documentation, memorization and circulation of the cognitive resources,
learning capacities and competencies that individuals and communities generate and use
in their professional contexts. Practices, like formal mentoring, monetary, or non-mone-
tary, reward for knowledge sharing and the allocation of resources to detect and capture
external knowledge, are examples of knowledge management.’’ [3]
The enormous changes that are reshaping the economy such as increased competition,
rapidly evolving technology, more capricious customers, the growth of the internet and
other factors are driving organizations to proactively manage their collective intellect [2]
via KM tools. This collective intellect, or Intellectual Capital (IC) with other words, is
the pursuit of effective use of knowledge (the finished product) as opposed to information
(the raw material) [4].
Although the importance of knowledge as a strategic asset can be traced back several
thousands of years, it was the ancient Egyptian and Greek civilizations that represented
the first evidence of the codification of knowledge for the purposes of leveraging regional
power with their implementations of national libraries and universities [5]. More recently,
Machlup coined the term ‘‘intellectual capital’’ in 1962 and used it to emphasize the impor-
tance of general knowledge as essential to growth and development [5]. IC includes assets
relating to employee knowledge and expertise, customer confidence in the company and its
products, brands, franchises, information systems, administrative procedures, patents,
trademarks and the efficiency of company business processes [6].
Today, IC is widely recognized as the critical source of true and sustainable competitive
advantage [7]. Knowledge is the basis of IC and is therefore at the heart of organizational
capabilities. Successfully utilizing that knowledge contributes to the progress of society [8].
IC was originally defined with three constructs (i.e. human capital, organizational cap-
ital and customer and relationship capital) [9], but some recent studies tend to rename cus-
tomer and relational capital as relational capital only [10–12]. See Fig. 1 [12] for an
illustrative definition of these constructs.
In this figure:
1. Human capital is the individual-level knowledge that each employee possesses [13].
2. Organizational capital is the sum of all assets that make the creative ability of the orga-
nization possible [11].
3. Relational capital is the sum of all assets that arrange and manage the firms’ relations
with the environment. The relational capital contains the relations with customers,
shareholders, suppliers, and rivals, the state, the official institutions and society [11].
F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147 125

3. The organizational dimension, which is the focus of this paper, is defined in the intel-
lectual capital as the organizational capital. The organizational capital is the sum of all
assets that make the creative ability of the organization possible. The mission of the firm,
its vision, basic values, strategies, working systems, and in-firm processes can be men-
tioned among these assets.
Organizational capital is one of the foundation stones of creating learning organiza-
tions. Even if the employees possess adequate or high capabilities, an organizational
structure that is made up of weak rules and systems and which cannot turn these capa-
bilities into a value, prevents the firm from having a high performance. On the contrary,
a strong organizational capital structure creates a supporting environment to its workers
and thus leads to workers’ risk taking even after their failures. Besides, it leads to the
decrease of the total cost and to the increase of the firm’s profit and productivity. There-
fore, the organizational capital is a vital structure for organizations and in an organiza-
tional level; it has a critical importance for the realization of measuring the intellectual
capital [4].
Most of the time, if not always, companies have limited resources. Defining measure-
ment indicators and their priorities for any important business activity helps companies
by providing a guideline for their efforts towards success. By using these priorities, man-
agers can decide in which activity they will invest first.
Many factors can be found in the literature to measure the organizational capital. Tan-
gible assets such as the patents of the firm, copyrights, databases, computer programs and
intangible assets such as the methods related to business management, company strategies,
and the culture of the company are some frequently used factors among these [11]. The
high investments of technology or the high number of computers and programs in a firm
are not a feature, which adds an additional value to a firm by itself. In order for these to
make a contribution to the company, the workers in the firm should have the abilities to
use these systems to interpret the results, to make them knowledge and to use them in the
relations [14]. As long as they are not in use, the existence of systems that possess and
transmit knowledge, which is the foundation stone of the organizational capital, cannot
effectively add value to the system. Therefore precise data concerning measurement indi-
cators of organizational capital are not available or very hard to be extracted [11]. In addi-
tion, decision-makers prefer natural language expressions rather than sharp numerical
values in assessing organizational capital parameters. So, organizational capital is an
INTELLECTUAL
CAPITAL
HUMAN CAPITAL
ORGANIZATIONAL
CAPITAL
RELATIONAL
CAPITAL
Individual-level knowledge Mission-vision Customers
Competence Strategical values Customer's loyalty
Leadership ability Working systems Market
Risk-taking and problem Culture Shareholders
solving capabilities Management system Suppliers
Education Use of knowledge Official institutions
Experience Databases Society
Fig. 1. Components of Intellectual Capital [12].
126 F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147

4. inherently fuzzy notion, which can be measured by the synthesis of its constituents. Fuzzy
logic offers a systematic base in dealing with situations, which are ambiguous or not well
defined. Indeed, the uncertainty in expressions such as ‘‘high level of the learning organi-
zations’’ or ‘‘moderate creative ability of the organization’’ which are frequently encoun-
tered in the organizational capital literature is fuzziness.
Prioritization of IC measurement indicators is a multi-attribute decision problem which
requires resolutions involved various stakeholders’ interests. In order to assist manage-
ment decision-making in selecting IC indicators for measurement and disclosure, Han
and Han [15] suggest a model that identifies the criteria reflecting decision usefulness
and expected risk factors. There has been no basis model for IC statements, nor bot-
tom-line indicators of the value of IC before [15].
This study aims at defining a methodology to improve the quality of prioritization of
organizational capital measurement indicators under uncertain conditions.
The paper is organized as follows: Section 2 defines the methodology of this research.
Section 3 includes a hierarchical model for prioritization of OC measurement indicators.
Section 4 includes a real-life numerical application. Finally, Section 5 presents the
conclusions.
2. Methodology
In the literature, there is only one paper aiming at prioritizing human capital measure-
ment indicators by using fuzzy AHP [16]. However, there is no fuzzy logic method aimed
at prioritizing organizational capital measurement indicators. As a value-added to the lit-
erature on the topic, this paper aims at providing practitioners with a fuzzy point of view
to the traditional intellectual capital analysis methods for dealing quantitatively with
imprecision or uncertainty and at obtaining a fuzzy prioritization of organizational capital
measurement indicators from this point of view that will close this gap considerably.
Fuzzy multi-criteria methods such as fuzzy TOPSIS, fuzzy AHP and fuzzy outranking
can solve such problems (see [17] for fuzzy multi-attribute decision making methods
and their applications). Unlike many other decision theories (such as most inventory
and scheduling models, linear programming, dynamic programming, etc.), MCDM meth-
odologies are controversial and there is not a unique theory accepted by everyone in the
field [18].
TOPSIS views a MADM problem with m alternatives as a geometric system with m
points in the n-dimensional space. It was developed by Hwang and Yoon [19]. The method
is based on the concept that the chosen alternative should have the shortest distance from
the positive-ideal solution and the longest distance from the negative-ideal solution. TOP-
SIS defines an index called similarity (or relative closeness) to the positive-ideal solution
and the remoteness from the negative-ideal solution. Then the method chooses an alterna-
tive with the maximum similarity to the positive-ideal solution [20].
The outranking decision aid methods compare all couples of actions. Instead of build-
ing complex utility functions, they determine which actions are being preferred to the oth-
ers by systematically comparing them on each criterion. The comparisons between the
actions lead to numerical results that show the concordance and/or the discordance
between the actions, and then allow to select or to sort the actions that can be compared.
F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147 127

5. The most well known outranking methods are ELECTRE, ORESTE, and PROMETHEE
[20–22].
AHP is developed by Saaty [23]. With this method, a complicated system is converted to
a hierarchical system of elements. In each hierarchical level, pair-wise comparisons of the
elements are made by using a nominal scale. These comparisons constitute a comparison
matrix. To find the weight of each element, or the score of each alternative, the eigenvector
of this matrix is calculated. At the end, the consistency of the pair-wise comparisons are
calculated by using a consistency ratio. If it is below a predefined level, the comparisons
are either revised by the decision-maker or excluded from the calculations.
In this paper, Fuzzy AHP will be preferred in the prioritization of organizational cap-
ital indicators since this method is the only one using a hierarchical structure among goal,
attributes and alternatives. Usage of pair-wise comparisons is another asset of this method
that lets the generation of more precise information about the preferences of decision-
makers. Moreover, since the decision-makers are usually unable to explicit about their
preferences due to the fuzzy nature of the decision process, this method helps them pro-
viding an ability of giving interval judgements instead of point judgements. Some recent
examples of fuzzy AHP applications can be found in [24–28].
There are several fuzzy AHP methods explained in the literature. Table 1 gives a com-
parison of these methods, which have important differences in their theoretical structures.
The comparison includes the advantages and disadvantages of each method. In this paper,
the authors prefer Chang’s extent analysis method [29,30] since the steps of this approach
are relatively easier than the other fuzzy AHP approaches and similar to the conventional
AHP.
In the following, the outlines of the extent analysis method on fuzzy AHP are given:
Let X = {x1,x2,. . .,xn} be an object set, and U = {u1,u2,. . .,um} be a goal set. Accord-
ing to Chang’s extent analysis [29,30], each object is taken and extent analysis for each
goal, gi, is performed respectively. Therefore, m extent analysis values for each object
can be obtained, with the following signs:
M1
gi
; M2
gi
; . . . ; Mm
gi
; i ¼ 1; 2; . . . ; n ð1Þ
where all the Mj
gi
ðj ¼ 1; 2; . . . ; mÞ are triangular fuzzy numbers (TFNs) whose para-
meters are a, b, and c. They are the lowest possible value, the most possible value, and
the largest possible value respectively. A TFN is represented as (a,b,c) as illustrated in
Fig. 2.
The steps of Chang’s extent analysis can be given as in the following:
Step 1. The value of fuzzy synthetic extent with respect to the ith object is defined as
Si ¼
X
m
j¼1
Mj
gi
X
n
i¼1
X
m
j¼1
Mj
gi
#1
ð2Þ
To obtain
Pm
j¼1Mj
gi
, perform the fuzzy addition operation of m extent analysis values for a
particular matrix such that
X
m
j¼1
Mj
gi
¼
X
m
j¼1
aij;
X
m
j¼1
bij;
X
m
j¼1
cij
!
; i ¼ 1; 2; . . . ; n ð3Þ
128 F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147

6. and to obtain
Pn
i¼1
Pm
j¼1Mj
gi
h i1
, perform the fuzzy addition operation of Mj
gi
j ¼ 1; 2;
ð
. . . ; mÞ values such that
X
n
i¼1
X
m
j¼1
Mj
gi
¼
X
n
i¼1
X
m
j¼1
aij;
X
n
i¼1
X
m
j¼1
bij;
X
n
i¼1
X
m
j¼1
cij
!
ð4Þ
and then compute the inverse of the vector in Eq. (4) such that
X
n
i¼1
X
m
j¼1
Mj
gi
#1
¼
1
Pn
i¼1
Pm
j¼1cij
;
1
Pn
i¼1
Pm
j¼1bij
;
1
Pn
i¼1
Pm
j¼1aij
!
ð5Þ
Table 1
The comparison of different fuzzy AHP methods [31]
Sources The main characteristics of the method Advantages (A) and disadvantages (D)
Van
Laarhoven
and Pedrycz
[32]
• Direct extension of Saaty’s AHP method
with triangular fuzzy numbers
• Lootsma’s logarithmic least
square method is used to derive fuzzy
weights and fuzzy performance scores
(A) The opinions of multiple
decision-makers can be modeled
in the reciprocal matrix
(D) There is not always a solution
to the linear equations
(D) The computational requirement
is tremendous, even for a
small problem
(D) It allows only triangular fuzzy
numbers to be used
Buckley [33] • Extension of Saaty’s AHP method
with trapezoidal fuzzy numbers
• Uses the geometric mean method to
derive fuzzy weights and
performance scores
(A) It is easy to extend to the
fuzzy case
(A) It guarantees a unique solution
to the reciprocal comparison matrix
(D) The computational requirement
is tremendous
Boender et al.
[34]
• Modifies van Laarhoven and
Pedrycz’s method
• Presents a more robust approach to
the normalization of the
local priorities
(A) The opinions of multiple
decision-makers can be modeled
(D) The computational requirement
is tremendous
Chang [29] • Synthetical degree values
• Layer simple sequencing
• Composite total sequencing
(A) The computational requirement
is relatively low
(A) It follows the steps of crisp
AHP. It does not involve
additional operations
(D) It allows only triangular fuzzy
numbers to be used
Cheng [35] • Builds fuzzy standards
• Represents performance scores by
membership functions
• Uses entropy concepts to calculate
aggregate weights
(A) The computational
requirement is not tremendous
(D) Entropy is used when
probability distribution
is known. The method is
based on both probability
and possibility measures
F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147 129

7. Step 2. The degree of possibility of M2 = (a2,b2,c2) P M1 = (a1,b1,c1) is defined as
V ðM2 P M1Þ ¼ sup
yPx
minðlM1
ðxÞ; lM2
ðyÞÞ
: ð6Þ
and can be equivalently expressed as follows:
V ðM2 P M1Þ ¼ hgtðM1 M2Þ ¼ lM2
ðdÞ ¼
1; if b2 P b1
0; if a1 P c2
a1 c2
ðb2 c2Þ ðb1 a1Þ
; otherwise
8
:
ð7Þ
where d is the ordinate of the highest intersection point D between lM1
and lM2
(see Fig. 3).
To compare M1 and M2, we need both the values of V(M1 P M2) andV(M2 P M1).
Step 3. The degree of possibility for a convex fuzzy number to be greater than k convex
fuzzy numbers Mi (i = 1,2,. . .,k) can be defined by
V ðM P M1; M2; . . . ; MkÞ ¼V ½ðM P M1Þ and ðM P M2Þ and and ðM P MkÞ
¼ min V ðM P MiÞ; i ¼ 1; 2; 3; . . . ; k: ð8Þ
1
a2 b2 a1 d c2 b1 c1
M2 M1
V(M2≥ M1)
Fig. 3. The intersection between M1 and M2.
μp (x)
1.0
0.0
y
X
a b c
a + (b-a) y c + (b-c) y
f1(.) f2(.)
Fig. 2. A triangular fuzzy number, ~
P ¼ ða; b; cÞ.
130 F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147

8. Assume that
d0
ðAiÞ ¼ min V ðSi P SkÞ ð9Þ
For k = 1,2,. . .,n; k 5 i. Then the weight vector is given by
W 0
¼ ðd0
ðA1Þ; d0
ðA2Þ; . . . ; d0
ðAnÞÞ
T
ð10Þ
where Ai (i = 1,2,. . .,n) are n elements.
Step 4. Via normalization, the normalized weight vectors are
W ¼ ðdðA1Þ; dðA2Þ; . . . ; dðAnÞÞ
T
ð11Þ
where W is a non-fuzzy number.
It is not possible to make mathematical operations directly on linguistic values. This is
why, the linguistic scale must be converted into a fuzzy scale. In the literature about fuzzy
AHP, one can find a variety of different fuzzy scales (see, for example, [28,36–38]). The
triangular fuzzy conversion scale given in Table 2 is used in the evaluation model of this
paper (adapted from [29]).
3. A hierarchical model for prioritization of OC measurement indicators
According to [4], organizational capital arises from processes and organizational value,
reflecting the external and internal focuses of the company, plus renewal and development
value for the future. A firm’s organizational capital includes its norms and guidelines, dat-
abases, organizational routines and corporate culture [10].
This study aims at defining a methodology to improve the quality of prioritization of
organizational capital measurement indicators under uncertain conditions. The method
chosen, fuzzy AHP, requires a hierarchical structure to yield with a result. Therefore,
the main attributes of the organizational capital are defined as deployment of the stra-
tegic values (DS), investments in the technology (IT) and flexibility of the organizational
structure (FS). The first main attribute, DS, is characterized with two sub-attributes:
Useableness of values in processes (UV) and fitness of values to daily working environ-
ment (FV). The second main attribute, IT, is characterized with three sub-attributes:
Reliability (RE), ease of use (EU), and relevance (RV). The last main attribute, FS, is
characterized with two sub-attributes: Supporting development (SD) and innovation
(IN).
Table 2
Triangular fuzzy conversion scale
Linguistic scale Triangular fuzzy scale Triangular fuzzy reciprocal scale
Just equal (1,1,1) (1,1,1)
Equally important (1/2,1,3/2) (2/3,1,2)
Weakly more important (1,3/2,2) (1/2,2/3,1)
Strongly more important (3/2,2,5/2) (2/5,1/2,2/3)
Very strongly more important (2,5/2,3) (1/3,2/5,1/2)
Absolutely more important (5/2,3,7/2) (2/7,1/3,2/5)
F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147 131

9. The hierarchical structure defined above serves to the aim of prioritization of the OC
measurement indicators. Ten indicators are selected [11], and defined as below:
IND1: Implementation rate of new ideas;
IND2: Quick access to information;
IND3: RD investment rate per employee;
IND4: Access to all information without any limitation;
IND5: Increasing rate of revenue per employee;
IND6: Updating rate of the databases;
IND7: MIS contains all information;
IND8: Decreasing rate of cost per revenue;
IND9: Knowledge sharing rate;
IND10: Index of transaction time of the processes.
Fig. 4 illustrates the hierarchical structure explained above.
Independency of judgment at each level is one of the basic axioms of AHP. It means
that a judgment at one level of hierarchy should be independent of the elements under
it. This axiom must be taken into account since the decision-makers tend to look at the
elements under the hierarchy while making evaluations. During the evaluation of this
study, the experts were guided to end up with an independent judgment.
If there were interdependence among criteria of different layers, Analytical Net-
work Process (ANP) would be used instead of AHP. ANP deals with such interdepen-
dence by obtaining the composite weights through the development of a ‘‘super matrix’’
[39].
4. A numerical application
To build the pair-wise comparison matrixes for the main and sub-attributes, and indi-
cators, some academics and professionals are worked. A questionnaire (see Appendix A) is
provided to get the evaluations. The results are calculated by taking the geometric mean of
DS
Selection of the
most efficient
indicators
FS
UV RE EU RV
IT
SD IN
IND1 IND2 IND10
FV
...
Fig. 4. Hierarchical structure of criteria.
132 F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147

10. individual evaluations. For the first step of the analysis, the pair-wise comparison matrix
for the main attributes is built (see Table 3).
For the first level (i.e. for main attributes), the values of fuzzy synthetic extents with
respect to the main attributes are calculated as below (see Eq. (2)):
SDS ¼ ð2:5; 3:17; 4Þ ð1=12:17; 1=9:83; 1=7:9Þ ¼ ð0:205; 0:322; 0:506Þ
SIT ¼ ð1:9; 2:17; 2:67Þ ð1=12:17; 1=9:83; 1=7:9Þ ¼ ð0:156; 0:220; 0:338Þ
SFS ¼ ð3:5; 4:5; 5:5Þ ð1=12:17; 1=9:83; 1=7:9Þ ¼ ð0:288; 0:458; 0:696Þ
The degrees of possibility are calculated as below (see Eq. (7)):
V ðSDS P SITÞ ¼ 1; V ðSDS 6 SITÞ ¼ 0:566
V ðSDS P SFSÞ ¼ 0:616; V ðSDS 6 SFSÞ ¼ 1
V ðSIT P SFSÞ ¼ 0:174; V ðSIT 6 SFSÞ ¼ 1
For each pair-wise comparison, the minimum of the degrees of possibility is found as be-
low: (see Eq. (8))
MinV SDS P Si
ð Þ ¼ 0:616
MinV SIT P Si
ð Þ ¼ 0:174
MinV SFS P Si
ð Þ ¼ 1:000
These values yield the following weights vector:
W 0
¼ ð0:616; 0:174; 1:000Þ
T
Via normalization, the importance weights (i.e. eigenvalues) of the main attributes are
calculated as follows:
W ¼ ðdðDSÞ; dðITÞ; dðFSÞÞT
¼ ð0:345; 0:097; 0:558Þ
At the second level, the weights of the sub-attributes of each main attribute are calcu-
lated. As can be seen from Fig. 4, DS has two sub-attributes; UV, and FV. The pair-wise
comparison for these two can be seen in Table 4.
The values of fuzzy synthetic extents with respect to DS are found as below:
ðUV; FVÞ ¼ ð0:684; 0:316Þ
The second main attribute in the model, IT, has three sub-attributes; RE, EU, and RV.
The pair-wise comparison for these three can be seen in Table 5.
Table 3
Pair-wise comparisons for main attributes
DS IT FS
DS (1,1,1) (1,3/2,2) (1/2,2/3,1)
IT (1/2,2/3,1) (1,1,1) (2/5,1/2,2/3)
FS (1,3/2,2) (3/2,2,5/2) (1,1,1)
F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147 133

11. The values of fuzzy synthetic extents with respect to IT are found as below:
ðRE; EU; RVÞ ¼ ð0:467; 0:212; 0:322Þ
The third main attribute in the model, FS, has two sub-attributes; SD, and IN. The
pair-wise comparison for these two can be seen in Table 6.
The values of fuzzy synthetic extents with respect to FS are found as below:
ðSD; INÞ ¼ ð0:320; 0:680Þ
For the third level, the pair-wise comparisons of indicators regarding to the sub-attri-
butes are calculated. The first sub-attribute to be taken into account is UV. Table 7 shows
the comparisons for that sub-attribute.
The values of fuzzy synthetic extents with respect to UV are found as below:
(Ind. 1, Ind. 2, Ind. 3, Ind. 4, Ind. 5, Ind. 6, Ind. 7, Ind. 8, Ind. 9, Ind. 10) = (0.122738,
0.076566, 0.07811, 0.128534, 0.008074, 0.130324, 0.114358, 0.019649, 0.137914,
0.183732).
The second sub-attribute to be taken into account is FV. Table 8 shows the compari-
sons for that sub-attribute.
The values of fuzzy synthetic extents with respect to FV are found as below:
(Ind. 1, Ind. 2, Ind. 3, Ind. 4, Ind. 5, Ind. 6, Ind. 7, Ind. 8, Ind. 9, Ind. 10) = (0.113086,
0.089316, 0.053684, 0.142309, 0.058197, 0.132163, 0.131783, 0.025734, 0.113823,
0.139904).
Table 5
Pair-wise comparison for the sub-attributes of IT
RE EU RV
RE (1,1,1) (1,3/2,2) (1,3/2,2)
EU (1/2,2/3,1) (1,1,1) (1/2,2/3,1)
RV (1/2,2/3,1) (1,3/2,2) (1,1,1)
Table 4
Pair-wise comparison for the sub-attributes of DS
UV FV
UV (1,1,1) (1,3/2,2)
FV (1/2,2/3,1) (1,1,1)
Table 6
Pair-wise comparison for the sub-attributes of FS
SD IN
SD (1,1,1) (1/2,2/3,1)
IN (1,3/2,2) (1,1,1)
134 F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147

12. Table 7
Pair-wise comparison for the indicators regarding to the sub-attribute UV
Ind. 1 Ind. 2 Ind. 3 Ind. 4 Ind. 5 Ind. 6 Ind. 7 Ind. 8 Ind. 9 Ind. 10
Ind. 1 (1,1,1) (3/2,2,5/2) (1,3/2,2) (1,3/2,2) (1,3/2,2) (2/3,1,2) (1/2,2/3,1) (1,3/2,2) (2/3,1,2) (2/5,1/2,2/3)
Ind. 2 (2/5,1/2,2/3) (1,1,1) (1,3/2,2) (1/2,2/3,1) (3/2,2,5/2) (1/2,2/3,1) (1/2,2/3,1) (1,3/2,2) (2/5,1/2,2/3) (2/5,1/2,2/3)
Ind. 3 (1/2,2/3,1) (1/2,2/3,1) (1,1,1) (1/2,2/3,1) (3/2,2,5/2) (1/2,2/3,1) (1/2,2/3,1) (3/2,2,5/2) (1/2,2/3,1) (2/5,1/2,2/3)
Ind. 4 (1/2,2/3,1) (1,3/2,2) (1,3/2,2) (1,1,1) (3/2,2,5/2) (2/3,1,2) (1,3/2,2) (3/2,2,5/2) (1/2,1,3/2) (1/2,2/3,1)
Ind. 5 (1/2,2/3,1) (2/5,1/2,2/3) (2/5,1/2,2/3) (2/5,1/2,2/3) (1,1,1) (2/5,1/2,2/3) (2/5,1/2,2/3) (1/2,1,3/2) (2/5,1/2,2/3) (2/5,1/2,2/3)
Ind. 6 (1/2,1,3/2) (1,3/2,2) (1,3/2,2) (1/2,1,3/2) (3/2,2,5/2) (1,1,1) (1,3/2,2) (3/2,2,5/2) (2/3,1,2) (2/5,1/2,2/3)
Ind. 7 (1,3/2,2) (1,3/2,2) (1,3/2,2) (1/2,2/3,1) (3/2,2,5/2) (1/2,2/3,1) (1,1,1) (3/2,2,5/2) (1/2,2/3,1) (2/5,1/2,2/3)
Ind. 8 (1/2,2/3,1) (1/2,2/3,1) (2/5,1/2,2/3) (2/5,1/2,2/3) (2/3,1,2) (2/5,1/2,2/3) (2/5,1/2,2/3) (1,1,1) (2/5,1/2,2/3) (1/3,2/5,1/2)
Ind. 9 (1/2,1,3/2) (3/2,2,5/2) (1,3/2,2) (2/3,1,2) (3/2,2,5/2) (1/2,1,3/2) (1,3/2,2) (3/2,2,5/2) (1,1,1) (1/2,2/3,1)
Ind. 10 (3/2,2,5/2) (3/2,2,5/2) (3/2,2,5/2) (1,3/2,2) (3/2,2,5/2) (3/2,2,5/2) (3/2,2,5/2) (2,5/2,3) (1,3/2,2) (1,1,1)
F.T.
Bozbura,
A.
Beskese
/
Internat.
J.
Approx.
Reason.
44
(2007)
124–147
135

13. Table 8
Pair-wise comparison for the indicators regarding to the sub-attribute FV
Ind. 1 Ind. 2 Ind. 3 Ind. 4 Ind. 5 Ind. 6 Ind. 7 Ind. 8 Ind. 9 Ind. 10
Ind. 1 (1,1,1) (1,3/2,2) (3/2,2,5/2) (2/3,1,2) (3/2,2,5/2) (1/2,2/3,1) (1/2,2/3,1) (3/2,2,5/2) (1/2,2/3,1) (2/5,1/2,2/3)
Ind. 2 (1/2,2/3,1) (1,1,1) (1,3/2,2) (1/2,2/3,1) (3/2,2,5/2) (2/5,1/2,2/3) (1/2,2/3,1) (3/2,2,5/2) (2/5,1/2,2/3) (2/5,1/2,2/3)
Ind. 3 (2/5,1/2,2/3) (1/2,2/3,1) (1,1,1) (2/5,1/2,2/3) (1/2,1,3/2) (1/2,2/3,1) (2/5,1/2,2/3) (1,3/2,2) (2/5,1/2,2/3) (2/5,1/2,2/3)
Ind. 4 (1/2,1,3/2) (1,3/2,2) (3/2,2,5/2) (1,1,1) (3/2,2,5/2) (1,3/2,2) (1,3/2,2) (2,5/2,3) (1,3/2,2) (1/2,1,3/2)
Ind. 5 (2/5,1/2,2/3) (2/5,1/2,2/3) (2/3,1,2) (2/5,1/2,2/3) (1,1,1) (1/2,2/3,1) (2/5,1/2,2/3) (1,3/2,2) (1/2,2/3,1) (2/5,1/2,2/3)
Ind. 6 (1,3/2,2) (3/2,2,5/2) (1,3/2,2) (1/2,2/3,1) (1,3/2,2) (1,1,1) (2/3,1,2) (3/2,2,5/2) (1,3/2,2) (1,3/2,2)
Ind. 7 (1,3/2,2) (1,3/2,2) (3/2,2,5/2) (1/2,2/3,1) (3/2,2,5/2) (1/2,1,3/2) (1,1,1) (3/2,2,5/2) (1,3/2,2) (1/2,1,3/2)
Ind. 8 (2/5,1/2,2/3) (2/5,1/2,2/3) (1/2,2/3,1) (1/3,2/5,1/2) (1/2,2/3,1) (2/5,1/2,2/3) (2/5,1/2,2/3) (1,1,1) (1/2,2/3,1) (2/5,1/2,2/3)
Ind. 9 (1,3/2,2) (3/2,2,5/2) (3/2,2,5/2) (1/2,2/3,1) (1,3/2,2) (1/2,2/3,1) (1/2,2/3,1) (1,3/2,2) (1,1,1) (1/2,2/3,1)
Ind. 10 (3/2,2,5/2) (3/2,2,5/2) (3/2,2,5/2) (2/3,1,2) (3/2,2,5/2) (1/2,2/3,1) (2/3,1,2) (3/2,2,5/2) (1,3/2,2) (1,1,1)
136
F.T.
Bozbura,
A.
Beskese
/
Internat.
J.
Approx.
Reason.
44
(2007)
124–147

14. Table 9
Pair-wise comparison for the indicators regarding to the sub-attribute RE
Ind. 1 Ind. 2 Ind. 3 Ind. 4 Ind. 5 Ind. 6 Ind. 7 Ind. 8 Ind. 9 Ind. 10
Ind. 1 (1,1,1) (2/5,1/2,2/3) (1,3/2,2) (2/5,1/2,2/3) (1,3/2,2) (2/5,1/2,2/3) (2/5,1/2,2/3) (3/2,2,5/2) (1/2,2/3,1) (1/2,2/3,1)
Ind. 2 (3/2,2,5/2) (1,1,1) (3/2,2,5/2) (1/2,2/3,1) (3/2,2,5/2) (1/2,2/3,1) (1/2,2/3,1) (2,5/2,3) (1,3/2,2) (1/2,1,3/2)
Ind. 3 (1/2,2/3,1) (2/5,1/2,2/3) (1,1,1) (1/3,2/5,1/2) (1,3/2,2) (1/3,2/5,1/2) (1/3,2/5,1/2) (1,3/2,2) (1/2,2/3,1) (1/2,2/3,1)
Ind. 4 (3/2,2,5/2) (1,3/2,2) (2,5/2,3) (1,1,1) (2,5/2,3) (2/3,1,2) (1/2,1,3/2) (2,5/2,3) (1,3/2,2) (1,3/2,2)
Ind. 5 (1/2,2/3,1) (2/5,1/2,2/3) (1/2,2/3,1) (1/3,2/5,1/2) (1,1,1) (1/3,2/5,1/2) (1/3,2/5,1/2) (1/2,1,3/2) (2/5,1/2,2/3) (2/5,1/2,2/3)
Ind. 6 (3/2,2,5/2) (1,3/2,2) (2,5/2,3) (1/2,1,3/2) (2,5/2,3) (1,1,1) (1,3/2,2) (5/2,3,7/2) (3/2,2,5/2) (3/2,2,5/2)
Ind. 7 (3/2,2,5/2) (1,3/2,2) (2,5/2,3) (2/3,1,2) (2,5/2,3) (1/2,2/3,1) (1,1,1) (2,5/2,3) (1,3/2,2) (3/2,2,5/2)
Ind. 8 (2/5,1/2,2/3) (1/3,2/5,1/2) (1/2,2/3,1) (1/3,2/5,1/2) (2/3,1,2) (2/7,1/3,2/5) (1/3,2/5,1/2) (1,1,1) (1/3,2/5,1/2) (1/3,2/5,1/2)
Ind. 9 (1,3/2,2) (1/2,2/3,1) (1,3/2,2) (1/2,2/3,1) (3/2,2,5/2) (2/5,1/2,2/3) (1/2,2/3,1) (2,5/2,3) (1,1,1) (1/2,2/3,1)
Ind. 10 (1,3/2,2) (2/3,1,2) (1,3/2,2) (1/2,2/3,1) (3/2,2,5/2) (2/5,1/2,2/3) (2/5,1/2,2/3) (2,5/2,3) (1,3/2,2) (1,1,1)
F.T.
Bozbura,
A.
Beskese
/
Internat.
J.
Approx.
Reason.
44
(2007)
124–147
137

15. Table 10
Pair-wise comparison for the indicators regarding to the sub-attribute EU
Ind. 1 Ind. 2 Ind. 3 Ind. 4 Ind. 5 Ind. 6 Ind. 7 Ind. 8 Ind. 9 Ind. 10
Ind. 1 (1,1,1) (2/5,1/2,2/3) (3/2,2,5/2) (1/3,2/5,1/2) (3/2,2,5/2) (1/2,2/3,1) (2/5,1/2,2/3) (3/2,2,5/2) (2/5,1/2,2/3) (1/2,1,3/2)
Ind. 2 (3/2,2,5/2) (1,1,1) (2,5/2,3) (1/2,2/3,1) (2,5/2,3) (1,3/2,2) (1,3/2,2) (2,5/2,3) (1/2,1,3/2) (1,3/2,2)
Ind. 3 (2/5,1/2,2/3) (1/3,2/5,1/2) (1,1,1) (1/3,2/5,1/2) (1,3/2,2) (2/5,1/2,2/3) (2/5,1/2,2/3) (3/2,2,5/2) (1/3,2/5,1/2) (1/2,2/3,1)
Ind. 4 (2,5/2,3) (1,3/2,2) (2,5/2,3) (1,1,1) (2,5/2,3) (1,3/2,2) (1,3/2,2) (5/2,3,7/2) (1/2,1,3/2) (3/2,2,5/2)
Ind. 5 (2/5,1/2,2/3) (1/3,2/5,1/2) (1/2,2/3,1) (1/3,2/5,1/2) (1,1,1) (1/3,2/5,1/2) (1/3,2/5,1/2) (1,3/2,2) (2/7,1/3,2/5) (1/3,2/5,1/2)
Ind. 6 (1,3/2,2) (1/2,2/3,1) (3/2,2,5/2) (1/2,2/3,1) (2,5/2,3) (1,1,1) (1/2,1,3/2) (2,5/2,3) (1/2,2/3,1) (1,3/2,2)
Ind. 7 (3/2,2,5/2) (1/2,2/3,1) (3/2,2,5/2) (1/2,2/3,1) (2,5/2,3) (2/3,1,2) (1,1,1) (2,5/2,3) (1/2,2/3,1) (1,3/2,2)
Ind. 8 (2/5,1/2,2/3) (1/3,2/5,1/2) (2/5,1/2,2/3) (2/7,1/3,2/5) (1/2,2/3,1) (1/3,2/5,1/2) (1/3,2/5,1/2) (1,1,1) (2/7,1/3,2/5) (2/5,1/2,2/3)
Ind. 9 (3/2,2,5/2) (2/3,1,2) (2,5/2,3) (2/3,1,2) (5/2,3,7/2) (1,3/2,2) (1,3/2,2) (5/2,3,7/2) (1,1,1) (2/5,1/2,2/3)
Ind. 10 (2/3,1,2) (1/2,2/3,1) (1,3/2,2) (2/5,1/2,2/3) (2,5/2,3) (1/2,2/3,1) (1/2,2/3,1) (3/2,2,5/2) (3/2,2,5/2) (1,1,1)
138
F.T.
Bozbura,
A.
Beskese
/
Internat.
J.
Approx.
Reason.
44
(2007)
124–147

16. Table 11
Pair-wise comparison for the indicators regarding to the sub-attribute RV
Ind. 1 Ind. 2 Ind. 3 Ind. 4 Ind. 5 Ind. 6 Ind. 7 Ind. 8 Ind. 9 Ind. 10
Ind. 1 (1,1,1) (2,5/2,3) (1/2,2/3,1) (2,5/2,3) (1/2,2/3,1) (3/2,2,5/2) (1,3/2,2) (2/5,1/2,2/3) (3/2,2,5/2) (2,5/2,3)
Ind. 2 (1/3,2/5,1/2) (1,1,1) (1/3,2/5,1/2) (1,3/2,2) (1/3,2/5,1/2) (1/2,1,3/2) (1/2,2/3,1) (2/7,1/3,2/5) (2/3,1,2) (1,3/2,2)
Ind. 3 (1,3/2,2) (2,5/2,3) (1,1,1) (2,5/2,3) (1/2,2/3,1) (3/2,2,5/2) (3/2,2,5/2) (2/5,1/2,2/3) (1,3/2,2) (2,5/2,3)
Ind. 4 (1/3,2/5,1/2) (1/2,2/3,1) (1/3,2/5,1/2) (1,1,1) (1/3,2/5,1/2) (2/3,1,2) (1/2,2/3,1) (2/7,1/3,2/5) (2/5,1/2,2/3) (1/2,1,3/2)
Ind. 5 (1,3/2,2) (2,5/2,3) (1,3/2,2) (2,5/2,3) (1,1,1) (2,5/2,3) (3/2,2,5/2) (1/2,2/3,1) (3/2,2,5/2) (5/2,3,7/2)
Ind. 6 (2/5,1/2,2/3) (2/3,1,2) (2/5,1/2,2/3) (1/2,1,3/2) (1/3,2/5,1/2) (1,1,1) (1/2,2/3,1) (2/7,1/3,2/5) (1/2,2/3,1) (1,3/2,2)
Ind. 7 (1/2,2/3,1) (1,3/2,2) (2/5,1/2,2/3) (1,3/2,2) (2/5,1/2,2/3) (1,3/2,2) (1,1,1) (1/3,2/5,1/2) (1/2,1,3/2) (2,5/2,3)
Ind. 8 (3/2,2,5/2) (5/2,3,7/2) (3/2,2,5/2) (5/2,3,7/2) (1,3/2,2) (5/2,3,7/2) (2,5/2,3) (1,1,1) (3/2,2,5/2) (5/2,3,7/2)
Ind. 9 (2/5,1/2,2/3) (1/2,1,3/2) (1/2,2/3,1) (3/2,2,5/2) (2/5,1/2,2/3) (1,3/2,2) (2/3,1,2) (2/5,1/2,2/3) (1,1,1) (3/2,2,5/2)
Ind. 10 (1/3,2/5,1/2) (1/2,2/3,1) (1/3,2/5,1/2) (2/3,1,2) (2/7,1/3,2/5) (1/2,2/3,1) (1/3,2/5,1/2) (2/7,1/3,2/5) (2/5,1/2,2/3) (1,1,1)
F.T.
Bozbura,
A.
Beskese
/
Internat.
J.
Approx.
Reason.
44
(2007)
124–147
139

17. Table 12
Pair-wise comparison for the indicators regarding to the sub-attribute SD
Ind. 1 Ind. 2 Ind. 3 Ind. 4 Ind. 5 Ind. 6 Ind. 7 Ind. 8 Ind. 9 Ind. 10
Ind. 1 (1,1,1) (3/2,2,5/2) (1,3/2,2) (1,3/2,2) (1/2,1,3/2) (1,3/2,2) (1,3/2,2) (1,3/2,2) (1,3/2,2) (1/2,2/3,1)
Ind. 2 (2/5,1/2,2/3) (1,1,1) (1/2,2/3,1) (2/3,1,2) (2/5,1/2,2/3) (2/3,1,2) (2/3,1,2) (2/5,1/2,2/3) (1/2,2/3,1) (1/3,2/5,1/2)
Ind. 3 (1/2,2/3,1) (1,3/2,2) (1,1,1) (1,3/2,2) (1/2,1,3/2) (1,3/2,2) (3/2,2,5/2) (1/2,1,3/2) (3/2,2,5/2) (1/2,2/3,1)
Ind. 4 (1/2,2/3,1) (1/2,1,3/2) (1/2,2/3,1) (1,1,1) (2/5,1/2,2/3) (2/3,1,2) (1/2,2/3,1) (2/5,1/2,2/3) (1,3/2,2) (1/3,2/5,1/2)
Ind. 5 (2/3,1,2) (3/2,2,5/2) (2/3,1,2) (3/2,2,5/2) (1,1,1) (1,3/2,2) (3/2,2,5/2) (1/2,1,3/2) (3/2,2,5/2) (1/2,2/3,1)
Ind. 6 (1/2,2/3,1) (1/2,1,3/2) (1/2,2/3,1) (1/2,1,3/2) (1/2,2/3,1) (1,1,1) (1,3/2,2) (1/2,2/3,1) (1,3/2,2) (2/5,1/2,2/3)
Ind. 7 (1/2,2/3,1) (1/2,1,3/2) (2/5,1/2,2/3) (1,3/2,2) (2/5,1/2,2/3) (1/2,2/3,1) (1,1,1) (1/2,2/3,1) (1/2,1,3/2) (2/5,1/2,2/3)
Ind. 8 (1/2,2/3,1) (3/2,2,5/2) (2/3,1,2) (3/2,2,5/2) (2/3,1,2) (1,3/2,2) (1,3/2,2) (1,1,1) (3/2,2,5/2) (1/2,2/3,1)
Ind. 9 (1/2,2/3,1) (1,3/2,2) (2/5,1/2,2/3) (1/2,2/3,1) (2/5,1/2,2/3) (1/2,2/3,1) (2/3,1,2) (2/5,1/2,2/3) (1,1,1) (1/3,2/5,1/2)
Ind. 10 (1,3/2,2) (2,5/2,3) (1,3/2,2) (2,5/2,3) (1,3/2,2) (3/2,2,5/2) (3/2,2,5/2) (1,3/2,2) (2,5/2,3) (1,1,1)
140
F.T.
Bozbura,
A.
Beskese
/
Internat.
J.
Approx.
Reason.
44
(2007)
124–147

18. Table 13
Pair-wise comparison for the indicators regarding to the sub-attribute IN
Ind. 1 Ind. 2 Ind. 3 Ind. 4 Ind. 5 Ind. 6 Ind. 7 Ind. 8 Ind. 9 Ind. 10
Ind. 1 (1,1,1) (2,5/2,3) (3/2,2,5/2) (3/2,2,5/2) (2,5/2,3) (3/2,2,5/2) (3/2,2,5/2) (5/2,3,7/2) (3/2,2,5/2) (1,3/2,2)
Ind. 2 (1/3,2/5,1/2) (1,1,1) (1/2,2/3,1) (1/2,2/3,1) (1,3/2,2) (2/5,1/2,2/3) (1/2,2/3,1) (1,3/2,2) (2/5,1/2,2/3) (1/2,2/3,1)
Ind. 3 (2/5,1/2,2/3) (1,3/2,2) (1,1,1) (1,3/2,2) (2,5/2,3) (3/2,2,5/2) (1,3/2,2) (2,5/2,3) (1/2,1,3/2) (1,3/2,2)
Ind. 4 (2/5,1/2,2/3) (1,3/2,2) (1/2,2/3,1) (1,1,1) (3/2,2,5/2) (1/2,1,3/2) (1/2,1,3/2) (2,5/2,3) (1/2,2/3,1) (3/2,2,5/2)
Ind. 5 (1/3,2/5,1/2) (1/2,2/3,1) (1/3,2/5,1/2) (2/5,1/2,2/3) (1,1,1) (2/5,1/2,2/3) (2/5,1/2,2/3) (1,3/2,2) (1/3,2/5,1/2) (2/5,1/2,2/3)
Ind. 6 (2/5,1/2,2/3) (3/2,2,5/2) (2/5,1/2,2/3) (2/3,1,2) (3/2,2,5/2) (1,1,1) (1/2,1,3/2) (2,5/2,3) (1/2,2/3,1) (1,3/2,2)
Ind. 7 (2/5,1/2,2/3) (1,3/2,2) (1/2,2/3,1) (2/3,1,2) (3/2,2,5/2) (2/3,1,2) (1,1,1) (2,5/2,3) (1/2,2/3,1) (1,3/2,2)
Ind. 8 (2/7,1/3,2/5) (1/2,2/3,1) (1/3,2/5,1/2) (1/3,2/5,1/2) (1/2,2/3,1) (1/3,2/5,1/2) (1/3,2/5,1/2) (1,1,1) (1/3,2/5,1/2) (2/5,1/2,2/3)
Ind. 9 (2/5,1/2,2/3) (3/2,2,5/2) (2/3,1,2) (1,3/2,2) (2,5/2,3) (1,3/2,2) (1,3/2,2) (2,5/2,3) (1,1,1) (3/2,2,5/2)
Ind. 10 (1/2,2/3,1) (1,3/2,2) (1/2,2/3,1) (2/5,1/2,2/3) (3/2,2,5/2) (1/2,2/3,1) (1/2,2/3,1) (3/2,2,5/2) (2/5,1/2,2/3) (1,1,1)
F.T.
Bozbura,
A.
Beskese
/
Internat.
J.
Approx.
Reason.
44
(2007)
124–147
141

19. The third sub-attribute to be taken into account is RE. Table 9 shows the comparisons
for that sub-attribute.
The values of fuzzy synthetic extents with respect to RE are found as below:
(Ind. 1, Ind. 2, Ind. 3, Ind. 4, Ind. 5, Ind. 6, Ind. 7, Ind. 8, Ind. 9, Ind. 10) = (0.063791,
0.137589, 0.030829, 0.173309, 0, 0.192902, 0.174788, 0, 0.104762, 0.122031).
The fourth sub-attribute to be taken into account is EU. Table 10 shows the compar-
isons for that sub-attribute.
The values of fuzzy synthetic extents with respect to EU are found as below:
(Ind. 1, Ind. 2, Ind. 3, Ind. 4, Ind. 5, Ind. 6, Ind. 7, Ind. 8, Ind. 9, Ind. 10) = (0.078642,
0.161791, 0.024112, 0.185463, 0, 0.131082, 0.138709, 0, 0.166405, 0.113795).
The fifth sub-attribute to be taken into account is RV. Table 11 shows the comparisons
for that sub-attribute.
The values of fuzzy synthetic extents with respect to RV are found as below:
(Ind. 1, Ind. 2, Ind. 3, Ind. 4, Ind. 5, Ind. 6, Ind. 7, Ind. 8, Ind. 9, Ind. 10) = (0.167738,
0.006464, 0.182739, 0, 0.223020, 0, 0.071391, 0.276315, 0.072332, 0).
The sixth sub-attribute to be taken into account is SD. Table 12 shows the comparisons
for that sub-attribute.
The values of fuzzy synthetic extents with respect to SD are found as below:
(Ind. 1, Ind. 2, Ind. 3, Ind. 4, Ind. 5, Ind. 6, Ind. 7, Ind. 8, Ind. 9, Ind. 10) = (0.132275,
0.057982, 0.123138, 0.058709, 0.139835, 0.076346, 0.055574, 0.131600, 0.047937,
0.176603).
Table 14
Priority weights of main and sub-attributes, and indicators
DS IT FS Weights
0.344645662 0.096988434 0.558365904
UV FV RE EU RV SD IN
0.684211 0.315789 0.466523 0.21163 0.321848 0.315789 0.684211
Ind. 1 0.122738 0.113086 0.063791 0.078642 0.167738 0.132275 0.216028 0.156842
Ind. 2 0.076566 0.089316 0.137589 0.161791 0.006464 0.057982 0.028529 0.058647
Ind. 3 0.07811 0.053684 0.030829 0.024112 0.182739 0.123138 0.157665 0.113803
Ind. 4 0.128534 0.142309 0.173309 0.185463 0 0.058709 0.119899 0.113605
Ind. 5 0.008074 0.058197 0 0 0.22302 0.139835 0 0.039856
Ind. 6 0.130324 0.132163 0.192902 0.131082 0 0.076346 0.119961 0.115826
Ind. 7 0.114358 0.131783 0.174788 0.138709 0.071391 0.055574 0.120076 0.109967
Ind. 8 0.019649 0.025734 0 0 0.276315 0.1316 0 0.039264
Ind. 9 0.137914 0.113823 0.104762 0.166405 0.072332 0.047937 0.165717 0.127086
Ind. 10 0.183732 0.139904 0.122031 0.113795 0 0.176603 0.072126 0.125104
142 F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147

20. The seventh sub-attribute to be taken into account is IN. Table 13 shows the compar-
isons for that sub-attribute.
The values of fuzzy synthetic extents with respect to IN are found as below:
(Ind. 1, Ind. 2, Ind. 3, Ind. 4, Ind. 5, Ind. 6, Ind. 7, Ind. 8, Ind. 9, Ind. 10) = (0.216028,
0.028529, 0.157665, 0.119899, 0, 0.119961, 0.120076, 0, 0.165717, 0.072126).
In the last stage of the analysis, overall priority weights of the indicators are calculated
as
(IND1, IND2, IND3, IND4, IND5, IND6, IND7, IND8, IND9, IND10) = (0.157,
0.059, 0.114, 0.114, 0.040, 0.116, 0.110, 0.039, 0.127, 0.125).
All of the results are summarized in Table 14.
5. Conclusion
The new millennium started a new era that can be called ‘‘era of knowledge’’. Managers
started to realize that the market value of their companies is not defined only by the tan-
gible assets any more. This is why IC, which is the sum of intangible assets of the com-
pany, has been one of the most popular concepts of this new era. Organizational
capital is one of the three dimensions of IC.
Defining measurement indicators and their priorities help companies by providing a
guideline for their efforts towards success. By using these priorities, managers can define
their roadmap in using their scarce resources in potential investments.
Since organizational capital is an intangible asset, the prioritization of its sub-
dimensions could successfully be handled with AHP. In this paper, the authors
proposed a Fuzzy AHP method to improve the quality of prioritization of organiza-
tional capital measurement indicators under uncertain conditions. To do so, a hierar-
chical model consisting of three main attributes, seven sub-attributes, and 10
indicators is built. The model is verbalized in a questionnaire form including pair-wise
comparisons.
The results calculated shows that the indicator Implementation rate of new ideas is
the most important indicator for organizational capital measurement. The companies
must pay full attention to implement newly created ideas and encourage the knowledge
creation process. The sequence of the rest of the indicators according to their impor-
tance weights is as follows: IND9-Knowledge sharing rate, IND10-Index of transaction
time of the processes, IND6-Updating rate of the databases, IND3-RD investment
rate per employee, IND4-Access to all information without any limitation, IND7-
MIS contains all information, IND2-Quick access to information, IND5-Increasing
rate of revenue per employee, IND8-Decreasing rate of cost per revenue. The weights
calculated can help companies in self-assessments, and constitute a basis for bench-
marking.
F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147 143

21. For further research, other fuzzy multi-criteria evaluation methods like fuzzy TOPSIS
or fuzzy outranking methods can be used and the obtained results can be compared with
the ones found in this paper.
Appendix A. Questionnaire forms used to facilitate comparisons of main and
sub-attributes
QUESTIONNAIRE
Read the following questions and put check marks on the pairwise comparison matrices. If an attribute on the
left is more important than the one matching on the right, put your check mark to the left of the importance “
Equal” under the importance level you prefer. If an attribute on the left is less important than the one matching
on the right, put your check mark to the right of the importance ‘Equal’ under the importance level you prefer.
QUESTIONS
With respect to the overall goal “prioritization of the organizational capital indicators”,
Q1. How important is deployment of the strategic values (DS) when it is compared with investment in
technology (IT)?
Q2. How important is deployment of the strategic values (DS) when it is compared with flexibility of the
organizational structure (FS)?
Q3. How important is investment in technology (IT) when it is compared with flexibility of the organizational
structure (FS)?
With
respect to:
the overall
goal
Importance (or preference) of one main-attribute over another
Questions
Attributes
Absolutely
More
Important
Very
Strongly
More
Important
Strongly
More
Important
Weakly
More
Important
Equally
Important
Just
Equal
Equally
Important
Weakly
More
Important
Strongly
More
Important
Very
Strongly
More
Important
Absolutely
More
Important
Attributes
Q1
Q2
DS
DS
IT
FS
Q3 IT FS
With respect to the main attribute “deployment of the strategic values (DS)”,
Q4. How important is useableness of values in processes(UV) when it is compared with fitness of values to daily
working environment (FV)?
With respect
to:
Deployment
of the str.
values
Importance (or preference) of one sub-attribute over another
√
√
√
144 F.T. Bozbura, A. Beskese / Internat. J. Approx. Reason. 44 (2007) 124–147

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Important
Very
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More
Important
Sub-attributes
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Absolutely
More
Important
Absolutely
More
Important
Absolutely
More
Important
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